Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22259 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C23×C11 | C2×#41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#97 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,25)(17,20)(18,23)(22,27)(24,26)(28,29,33,37,34,38,32,42)(30,35,40,43,39,36,31,41);(12,14)(13,18)(15,24)(16,22)(17,23)(19,27)(20,21)(25,26)(28,30,33,40,34,39,32,31)(29,35,37,43,38,36,42,41);(12,15,17,16)(13,19,20,25)(14,22,23,24)(18,26,21,27)(28,31,32,39,34,40,33,30)(29,36,37,41,38,35,42,43);(12,16,17,15)(13,19,20,25)(14,22,23,24)(18,27,21,26)(30,39)(31,40)(35,36)(41,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15247);